• 대한수학회지
• /
• 제36권1호
• /
• pp.209-227
• /
• 1999

We propose new parallel block ILU (Incomplete LU) factorization preconditioners for a nonsymmetric block-tridiagonal M-matrix. Theoretial properties of these block preconditioners are studied to see the convergence rate of the preconditioned iterative methods, Lastly, numerical results of the right preconditioned GMRES and BiCGSTAB methods using the block ILU preconditioners are compared with those of these two iterative methods using a standard ILU preconditioner to see the effectiveness of the block ILU preconditioners.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제23권3호
• /
• pp.267-282
• /
• 2019

This paper examines how one can build a block tridiagonal structure for k-almost normal matrices and also for k-almost conjugate normal matrices. We shall see that these representations are created by unitary similarity and unitary congruance transformations, respectively. It shall be proven that the orders of diagonal blocks are 1, k + 2, 2k + 3, ${\ldots}$, in both cases. Then these block tridiagonal structures shall be reviewed for the cases where the mentioned matrices satisfy in a second-degree polynomial. Finally, for these processes, algorithms are presented.

• Journal of applied mathematics & informatics
• /
• 제8권3호
• /
• pp.705-720
• /
• 2001

We propose a variant of parallel block incomplete factorization preconditioners for a symmetric block-tridiagonal H-matrix. Theoretical properties of these block preconditioners are compared with those of block incomplete factoriztion preconditioners for the corresponding somparison matrix. Numerical results of the preconditioned CG(PCG) method using these block preconditioners are compared with those of PCG using other types of block incomplete factorization preconditioners. Lastly, parallel computations of the block incomplete factorization preconditioners are carried out on the Cray C90.

• 대한수학회보
• /
• 제37권3호
• /
• pp.551-568
• /
• 2000

We propose new parallelizable block incomplete factorization preconditioners for a symmetric block-tridiagonal H-matrix. Theoretical properties of these block preconditioners are compared with those of block incomplete factorization preconditioners for the corresponding comparison matrix. Numerical results of the preconditioned CG(PCG) method using these block preconditioners are compared with those of PCG method using a standard incomplete factorization preconditioner to see the effectiveness of the block incomplete factorization preconditioners.

• 한국통신학회논문지
• /
• 제15권7호
• /
• pp.553-564
• /
• 1990

선계2계 편미분 방정식의 일반식에 대한 계수 메트릭스를 (n-1)x(n-1) submatrices로 나누어서 block tridiagonal system으로 변환한 후 cyclic odd-even reduction 기법을 응용하여 large-grain data granularity로서 미지벡타를 구하는 block cyclic reduction 알고리즘을 작성했다. 그런데 이 block cyclic reduction 기법은 매 연산의 단계마다 병렬성이 변하여 병렬처리형 컴퓨터에는 적합하지 못하므로 이 기법을 변형해서 병렬성이 일정하며 실행시간이 보다 단축되는 block cyclic reduction 기법을 제안하고 이 기법에 의한 선형2계 편미분 방정식의 일반식의 解를 구하는 알고리즘을 작성하여 기존의 기법과 비교 고찰했다.

• Journal of applied mathematics & informatics
• /
• 제6권2호
• /
• pp.455-466
• /
• 1999

In this note we present a numerical scheme for finding an approxximate solution of an equation which can be viewed as a model for spatial diffusion of age-depednent biological populations. Discretization of the model yields a linear system with a block tridi-agonal matrix. Our main concern will be discussion of stability for this scheme by examining the eigenvalues of the block tridiagonal matrix. Numerical results are presented.

• 산업기술연구
• /
• 제14권
• /
• pp.19-28
• /
• 1994

일반적으로 2차원 Poisson 방정식을 풀기 위해 유한 차분법을 이용하여 tridiagonal block Toeplitz 선형방정식을 얻는다. 이 선형방정식의 독특한 형태를 활용하기 위해 Lyapunov 방정식으로 변화시킨 다음 이산정현변환(DST)을 이용해서 대각선 행렬로 만들면 계산이 용이해진다. 또 DST는 FFT를 이용해 계산할 수 있으므로 고속 계산이 가능하다. FFT를 병렬로 처리하기 위해 프로세서가 4,096개인 SIMD 컴퓨터 MP-2에서 시뮬레이션했다. 본 논문에서는 알고리즘 유도, 매핑 및 시뮬레이션 결과를 제시했다.

• 대한산업공학회지
• /
• 제11권2호
• /
• pp.1-9
• /
• 1985

In this study, two stage transfer line with limited repair capability is modeled to formulate optimal dynamic repair priority policy. The method of Markov Chains is used to analyze the analytical model of this line. An efficient algorithm is developed, utilizing the block tridiagonal structure of the transition probability matrix, to obtain the steady state probabilities and system performance measures, such as the steady state production rate of the line and the average in-process inventory in the interstage buffer.

• 대한수학회보
• /
• 제55권3호
• /
• pp.881-898
• /
• 2018

This article deals with implementation of a high-order finite difference scheme for numerical solution of the incompressible Navier-Stokes equations on curvilinear grids. The numerical scheme is based on pseudo-compressibility approach. A fifth-order upwind compact scheme is used to approximate the inviscid fluxes while the discretization of metric and viscous terms is accomplished using sixth-order central compact scheme. An implicit Euler method is used for discretization of the pseudo-time derivative to obtain the steady-state solution. The resulting block tridiagonal matrix system is solved by approximate factorization based alternating direction implicit scheme (AF-ADI) which consists of an alternate sweep in each direction for every pseudo-time step. The convergence and efficiency of the method are evaluated by solving some 2D benchmark problems. Finally, computed results are compared with numerical results in the literature and a good agreement is observed.